141 LearnersLast updated on May 26th, 2025
Square Root of 100000
If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in the field of vehicle design, finance, etc. Here, we will discuss the square root of 100000.
What is the Square Root of 100000?
The square root is the inverse of the square of a number. 100000 is not a perfect square. The square root of 100000 is expressed in both radical and exponential form. In the radical form, it is expressed as √100000, whereas (100000)^(1/2) in the exponential form. √100000 = 316.227766, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 100000
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where long-division method and approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 100000 by Prime Factorization Method
The product of prime factors is the Prime factorization of a number. Now let us look at how 100000 is broken down into its prime factors:
Step 1: Finding the prime factors of 100000 Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5: 2^5 x 5^4
Step 2: Now that we have found the prime factors of 100000, the second step is to make pairs of those prime factors.
Since 100000 is not a perfect square, calculating its square root using prime factorization directly is not feasible.
Square Root of 100000 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.
Step 1: To begin with, we need to group the numbers from right to left. In the case of 100000, we need to group it as 00, 00, and 10.
Step 2: Now we need to find n whose square is less than or equal to 10. We can say n is ‘3’ because 3 × 3 = 9, which is less than 10. Now the quotient is 3, and after subtracting 9 from 10, the remainder is 1.
Step 3: Bring down the next pair of digits (00) to the right of the remainder, making it 100.
Step 4: The new divisor will be the sum of the old divisor and the quotient, which is 6 (3 + 3). Now we need to find n such that 6n × n ≤ 100.
Step 5: Let n be 1, then 61 × 1 = 61, and subtract 61 from 100 to get 39.
Step 6: Bring down the next pair of digits (00) to make it 3900.
Step 7: The new divisor is 62 (61 + 1), and we need to find n such that 62n × n ≤ 3900.
Step 8: Let n be 6, then 626 × 6 = 3756, and subtract 3756 from 3900 to get 144.
Step 9: Add a decimal point and bring down two zeros, making it 14400.
Step 10: Continue this process until you reach the desired decimal places.
So the square root of √100000 is approximately 316.2277.
Square Root of 100000 by Approximation Method
The approximation method is another method for finding square roots; it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 100000 using the approximation method.
Step 1: Now we have to find the closest perfect square of √100000. The smallest perfect square less than 100000 is 96100 (310^2), and the largest perfect square greater than 100000 is 102400 (320^2). √100000 falls somewhere between 310 and 320.
Step 2: Now we need to estimate the value between these two perfect squares. We can see that 100000 is closer to 102400 than it is to 96100, so a value closer to 316 is reasonable.
Step 3: Using the approximation, we find the square root of 100000 to be approximately 316.2277.
Common Mistakes and How to Avoid Them in the Square Root of 100000
Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping long division methods. Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number has both positive and negative square roots. However, we generally consider only the principal (positive) square root in practical applications.
For example, √10000 = 100, but there is also -100, which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root symbol properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important before moving to the next step.
For example, √(100 + 900) = √100 + √900 is incorrect. The correct way is √(100 + 900) = √1000.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value.
For example, √50 = 7 is incorrect; the correct answer is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly, as this will help them avoid mistakes.
For example, √1000 and ∛1000 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, many students might skip a step accidentally, which results in a wrong answer at the end of the problem. This may happen during subtraction or elsewhere.
Square Root of 100000 Examples
Problem 1
Can you help Max find the length of a side of a square field if its area is 100000 square meters?
The length of a side of the square field is approximately 316.23 meters.
Explanation
The area of the square = side^2,
If the area is 100000 square meters, then the side length = √100000 ≈ 316.23 meters.
Problem 2
A square-shaped building measuring 100000 square feet is built; if each of the sides is √100000, what will be the square feet of half of the building?
50000 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 100000 by 2 gives us 50000.
So half of the building measures 50000 square feet.
Problem 3
Calculate √100000 x 5.
1581.14
Explanation
The first step is to find the square root of 100000, which is approximately 316.23.
The second step is to multiply 316.23 by 5.
So 316.23 x 5 = 1581.14.
Problem 4
What will be the square root of (100000 + 2400)?
The square root is approximately 320.
Explanation
To find the square root, we need to find the sum of (100000 + 2400).
100000 + 2400 = 102400, and then √102400 = 320.
Therefore, the square root of (100000 + 2400) is ±320.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √100000 units and the width ‘w’ is 50 units.
We find the perimeter of the rectangle as approximately 732.46 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√100000 + 50)
= 2 × (316.23 + 50)
= 2 × 366.23
= 732.46 units.
FAQ on Square Root of 100000
1.What is √100000 in its simplest form?
2.Mention the factors of 100000.
3.Calculate the square of 100000.
4.Is 100000 a prime number?
5.100000 is divisible by?
6.How does learning Algebra help students in Oman make better decisions in daily life?
7.How can cultural or local activities in Oman support learning Algebra topics such as Square Root of 100000?
8.How do technology and digital tools in Oman support learning Algebra and Square Root of 100000?
9.Does learning Algebra support future career opportunities for students in Oman?
Important Glossaries for the Square Root of 100000
- Square root: A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4 because 4 × 4 = 16.
- Irrational number: An irrational number cannot be expressed as a simple fraction; its decimal goes on forever without repeating. √100000 is irrational.
- Principal square root: This refers to the positive square root of a number. For example, the principal square root of 100000 is approximately 316.23.
- Prime factorization: A way of expressing a number as the product of its prime factors. For instance, the prime factorization of 100000 is 2^5 × 5^4.
- Perimeter: The total length around a two-dimensional shape. For example, the perimeter of a rectangle is calculated as 2 × (length + width).
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Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
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